Comparing Options

Question 1

What is the maximum price of a European Call Option?

Answer 1

F^P(S)

Question 2

What is the minimum price of a European Call Option?

Answer 2

max(0, F^P(S) - Ke^-rT)

Question 3

What is the maximum price of a American Call Option?

Answer 3

S

Question 4

What is the minimum price of a American Call Option?

Answer 4

max(0, S - K)

Question 5

What is the maximum price of a European Put Option?

Answer 5

Ke^-rT

Question 6

What is the minimum price of a European Put Option?

Answer 6

max[0, Ke^-rT - F^P(S)]

Question 7

What is the maximum price of a American Put Option?

Answer 7

K

Question 8

What is the minimum price of a American Put Option?

Answer 8

max(0, K - S)

Question 9

When is early exercise optimal for a Call Option on a

Dividend paying stock?

Answer 9

Early exercise is optimal if:

PV(Divs) > PV(Interest on K) + Implicit Put

Question 10

When is early exercise optimal for a Call Option on a

Non-Dividend paying stock?

Answer 10

Early exercise is never optimal.

C_Amer = C_Eur

Question 11

When is early exercise optimal for a Put_ Option_ on a

Dividend paying stock?

Answer 11

Early exercise is optimal if:

PV(Interest on K) > PV(Divs) + Implicit Call

Question 12

When is early exercise optimal for a Put_ Option_ on a

Non-Dividend paying stock?

Answer 12

Early exercise is optimal if:

PV(Interest on K) > PV(Divs) + Implicit Call

Question 13

For K₁ < K₂ < K₃

Arrange the corresponding Put Premiums by size, from Largest to Smallest.

Answer 13

P(K3) > P(K₂) > P(K1)

Question 14

For K₁ < K₂ < K₃

Arrange the corresponding Call Premiums by size, from Largest to Smallest.

Answer 14

C(K₁) > C(K₂) > C(K₃)

Question 15

For K₁ < K₂ < K₃

What is the maximum value of C(K₁) - C(K₂) for American Calls?

Answer 15

K₂ -K₁

Question 16

For K₁ < K₂ < K₃

What is the maximum value of C(K₁) - C(K₂) for European Calls?

Answer 16

PV(K₂ -K₁)

Question 17

For K₁ < K₂ < K₃

What is the maximum value of P(K₂) - P(K₁) for American Puts?

Answer 17

K₂ -K₁

Question 18

For K₁ < K₂ < K₃

What is the maximum value of P(K₂) - P(K₁) for European Puts?

Answer 18

PV(K₂ -K₁)

Question 19

For K₁ < K₂ < K₃

What inequality must hold true for all Calls?

Answer 19

Question 20

For K₁ < K₂ < K₃

What inequality must hold true for all Puts?

Answer 20